Instability of a viscoelastic swirling liquid jet in static ambient gas is studied theoretically and numerically. The theoretical model is established based on the azimuthal Rankine vortex and axial nonuniform velocity distribution, enabling the initially unrelaxed elastic stress in the axial direction of the jet. Linear instability analysis is carried out to study the transition of predominant modes through comparing the maximum perturbation growth rates between different azimuthal modes, and energy budget analysis is employed to reveal the physical mechanism of modes transition. As the rotation is slow, the jet instability is dominated by the unrelaxed axial elastic stress, thus resulting in axisymmetric evolution of the liquid jet. However, when the jet rotates faster, the effect of unrelaxed axial elastic stress weakens rapidly, while the centrifugal force which originates from the inertial effect of the swirling jet starts to play a primary role, leading to the predominant modes transition to larger azimuthal wave numbers. With the enhancement of liquid elasticity, the jet instability would be dominated by a larger azimuthal wave number. To further identify the effect of elastic force on jet instability quantitatively, the numerical simulations based on the open-source platform Basilisk are carried out. It is found that the elastic force plays a stabilizing role on axial, radial, and azimuthal directions of the swirling jet. However, this stabilizing effect weakens with the enhancement of elasticity, leading to the increase of jet kinetic energy with a quicker growth of disturbance at jet interface. Moreover, the centrifugal force and the Coriolis force increases with the enhancement of elasticity, thereby promoting the predominant modes transition to larger azimuthal wave numbers.

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• Flow instability
• Interfacial flows
• Non-Newtonian fluids
• Viscoelasticity
• Navier-Stokes equation
• Volume of fluid method